The document discusses how Leonardo Da Vinci's Vitruvian Man and the proportions found in nature, such as the Fibonacci sequence and the Golden Rectangle, are used to create beautiful designs. It provides many examples of how proportions of 62% are used in architecture like the Parthenon and Notre Dame, as well as art, design of objects like chairs and kitchens, and the human face and body. Diagonal lines and placement are also discussed as techniques to direct attention and create movement, balance, and harmony.

1. Learn How Da Vinci’s
Golden Proportions
Create Beautiful Designs
Mark Rosenhaus, CKD

2. Leonardo Da Vinci’s Vitruvian Man is the familiar icon of proportion. The
width of the outstretched arms equals his height (within the square). The chest
is 62% of the arms. A perfect star fits within the circle using the same

3. The geometry in nature is found in the sequence of Fibonacci Numbers.
Find the pattern, then dividing adjacent numbers produces 62%.
The Golden Rectangle proportion has the width 62% of its length.

4. Drawing the Nautilus Golden Rectangle: Begin with a 1x1 square (ACc) , add a
smaller (cDd) square 62% of the original square. This will produce a Golden Rectangle,
where the width is 62% of it’s length (1:1.62). Add another square (dBe) 62% of the
second square, followed by (efh) which is 62% of the previous square, and so on.
Scribe an arc from A - c, then another arc from c - d, then d - e, e - f, f - g and g - h to
complete the spiral.

5. Spiral of the galaxies
The spiral of the galaxies is the same swirl as the Nautilus and the side of your

6. 1.62
DNA building block pattern repeats within a square and Golden
Rectangle.
With the 62% proportion in our DNA, it is obvious we find it so pleasing.

7. Fibonacci proportions of the finger: The first digit is 62%
of the second digit, which is 62% of the third.
The total length of the first two digits equals the third digit.

8. Michelangelo’s “David”
has a beautiful body.
The floor to navel
distance is 62% of his
height. At birth the navel
is in the middle of the
body. Boys at 13 years
may also have perfect
proportions, then
between 13 - 17 their
proportions will vary until
growth stops. My son at
13 had perfect
proportions, then his legs
grew more and now we
say he has long legs.
62%

9. Audrey Hepburn – Perfect face
A square is formed as the width of her
face equals the height from chin to
eyebrows. Another square is formed
from the corners of her mouth up to the
underside of her eyes. A Golden
Rectangle is the width of her face, then
from chin to the top of her head.
Each cheek width is 62% of her mouth
as is the chin to mouth distance, and
from the underside of her eyes to the top
of her eyebrows. Most women have nice
size cheeks, but a large chin distance
makes a long face while the eye area is
usually too small. Some women shave,
then redraw their eyebrows higher.
Drawing diagonal lines through the two
squares of her face intersect at the tip of
her nose. An arc from her nose to the
corners of her mouth delineates the
curve of her lower lip.

10. Fish Proportions: The main body is a Golden Rectangle, 1.00 unit x 1.618 (1.62) units.
The remaining tail section is 1 x 1. The mouth is at 62% of the body height.

11. Fibonacci Flying Formation : 1, 1, 2, 3, 5, 8, 13, 21, 34,
55, ...
Count the number of birds in each group.
2 8 3 1
5 1 3 5 2 1

12. Sunflower spirals in a clockwise direction count 34; counter clockwise, 55.
Exactly 62% Fibonacci Numbers.

13. .62 .621.00
Stonehenge Golden Proportions: The distance from the outer ring to the center
stones is 62% of the distance between the center stones.
Once again, proportions similar to our mouth-to-cheek distance.

14. Parthenon columns are 62% of the height to the peak

15. Why is a Greek urn beautiful?
Similar to the face, the width is
62% of the height as are the upper
and lower sections 62% of the
middle. Good decoration
emphasizes form, as provided by
the figures. The width of the outer
portion of the spout (17.5) is 62%
of the inside diameter (11.6).
The three segments of the lower
portion (above the base), are in
Fibonacci sequence.

16. The Space Shuttle’s wingspan
and length are 78 feet and 122 feet
-
a 64% ratio. (62% might have
prevented its problems.)

17. 62%
Previously the portrait was centered on the $10 note. Now, the distance from the right
edge to the right eyebrow – which is the focal point – is 62% of the total length of the bill

18. .62 1.00 .62
100%
62%

19. The Cathedral of Notre Dame
is designed within a Golden
Rectangle. A square defines the
lower portion. The size and
placement of the rosette is tangent
to the diagonals of the square and
the larger Golden Rectangle. The
bottom of the rosette is at the
midpoint of the square – just as the
eye is on a face.

20. The Taj Mahal entrance is a square flanked by Golden Rectangles. The overall
size is determined by diagonals from the base to the outer sides forming a
square. The distance above the door is 62% of it’s height.

21. 27x15 + 27x27 = 27”x42” 42”x42” 27”x42”
The glass doors form a square with Golden Rectangles on each side that are
divided into a double door square and a horizontal Golden Rectangle. When the
owners were told these are the same proportions as the Taj Mahal, they were
awestruck, understanding the importance this relationship brings to their kitchen.

22. Georges Seurat skillfully positions precisely sized objects around the canvas
to direct the scene. From the center red umbrella the man to its left is looking
tangent to it towards the tree, then down between the seated girls. From the
black umbrella in the upper right, a diagonal goes through those girls as the
dog’s tail and nose are exactly on the line.

23. Jan Vermeer balances, locates
and sizes the chandelier with
well placed objects. Generating
lines through the stool leg, the
painter’s right leg and the easel
direct the viewer to the edges of
the chandelier.

24. Generating lines locate and size objects.
Generating lines locate and size the keystone, the window and angle of the door

25. Empire State Building.
The focal point is designed
within a square.
Generating Lines cross at
strategic points to
determine location of
windows, decoration and
change in setbacks.
Outside corners of the
building guide to the top of
the tower. Placement, as
well as proportion, create
a lasting impression.
1.00
.38
.62

26. Generating lines help locate, size and compose a wall grouping that
culminates at the focal point. Furniture is located in relation to the length of the
wall. Accessories are proportional to the furniture. The arrangement has
direction.

27. The original definition
of symmetry was the
balance of harmony and
proportion based on weight
and mass.
A ballerina in the
arabesque position is
balanced at the center of
gravity of the sacrum,
upheld by the tip of her toe
and one outstretched leg;
she moves and the beauty
of the moment is gone.
The modern definition has
regressed into the idea of
axial (or mirror) symmetry –
a vertical line with two
items equidistant from each
side. This works with small
objects or only minimal
time to understand the
design. On a large scale it
is monotonous.

28. My first Golden Proportion kitchen.
Each upper cabinet is a Golden Rectangle
(G.R.) They are different sizes, yet the
same proportion. (See the dimensions,
above.) The entire group fits within a G.R.
The middle cabinet along with the shelf is
a square and forms a G.R. with the
cabinet to its right. Diagonal lines cross in
the center of the middle cabinet – right
where the eye wants to go – confirming
correct proportions.

29. The pantry width is 62% of the star cabinet, which is 62% of the hood space.
The top of the hood is half the bottom width. The curve of the hood leads to the corner
of the counter top. A line drawn from the top corner of the hood passes through the star
cabinet knobs, then diagonally across the lower pantry door to the counter top. The
bottom of the star cut out is the midpoint of the door – similar to the eye on a face.

30. Dynamic symmetry is an ‘X’ formed by the thrust of his arms
towards her legs, then his left toe to her elbow to the upper right.

31. Notice the difference where the photos
are cropped. In the left picture, his hand
points directly to the corner. Not so in the
upper photo. His arm to hers glides to the
lower corner as the curve of his leg to her
chest guides to the upper left. We are, at
first, attracted to his face in the center of
the picture which gazes at hers. Though
their bodies are not centered, the picture is
balanced as you feel their vitality and
movement.
The upper photo… static.

32. Mies Van Der Rohe. The chair is designed within a square. The proportions of the back
and seat are also squares. Arcs from the corner and mid point determine the curves.

33. Golden Rectangles and a square whirl in balance - as on a see-saw.

34. Variations on the golden rectangle theme.

35. The glass inserts are in 62% width and height proportion to the door.
They guide your view upward to the horizontal lift up doors then
across to the Golden Rectangle and down. A double square over the
cooktop leads up to the square completing the spiral arrangement.

36. Schematic of the previous cabinetry composition using squares, double
squares and Golden Rectangles.

37. 100%
62%
50%
Where do you find inspiration?
Robie House, Frank Lloyd Wright horizontals and overhangs.
Half the width of the house is at the chimney and the left edge of the peaked roof.
The distance from the left end of the eave to the peak of the roof is 62% of the house.

38. Fallingwater. Dynamic, spiral movement of the square fireplace moving to the right to
the double square stone wall, up either square block, then across the horizontal lines
and back down the small stone wall.

39. Frank Lloyd Wright inspired eaves, recesses and multiple levels.
The thrust of the composition is from the heavier pantry to the open shelf. The cabinets
follow the proportions of the finger. The open shelf is 62% of the angled louvered doors,
which is 62% of the triple door cabinet. The shelves and angled cabinet equal the width
of the glass cabinet. The pantry upper door is a square which fits into the Golden
Rectangle lower door.
18” 30”
48”

40. 62% Fibonacci sequence: 18”, 30”, 48”.
48”
30”
18”

41. The Golden Proportion kitchen cabinets continue into the dining room with a
square open space and Golden Rectangle glass cabinet. Together they form a larger
Golden Rectangle. Even the base cabinets are 30” and 48” Golden Proportion.
21”
34”
55” 48”
30”

42. 3-2-1, 62% sequence
of the upper doors.
55”
34”
21”

43. Diagonal lines go through key
points of the design as shown
by the dots on corners of the
cabinets. The curve of the top
cabinet hits two other corners
to confirm exact diameter.

44. The four squares are set in the cabinet as eyes on a face. The bottom of
the cut out is at the midpoint of the door. The space on each side of the cut
out is 62% of the opening. The top upper doors are all squares.

45. The cabinets are
arranged in groups
similar to instruments in
an orchestra for stronger
visual continuity. (Wood,
steel and blue glass.)
The upper and lower
glass doors are
proportional to the face,
as the width of the wood
area is 62% of the glass.
The upper door is a
square that fits into the
lower Golden Rectangle.

46. Piet Mondrian
perfectly places shapes
with the visual strength
of color guiding the
viewer around the
canvas. Starting with
the red square, step
down the two black
shapes then up the
blue and finally to the
yellow which completes
the spiral.

47. Three Dimensional
‘Mondrian’:
A spiral pattern similar to the
Nautilus seashell begins with
sliding glass doors, up a Golden
Rectangle, across a double
square (lift up door), continuing
to a larger double square and
ending with a smaller square
half the height of the large
square.

48. The curve and circle are
reminiscent of a Joan Miro
painting. The entire cabinet is
a square. The swerved doors
are within a Golden
Rectangle. The center of the
circle aligns with the
intersection of the upper and
lower curves.

49. Three glass squares and a glass Golden Rectangle surround the horizontal lift up

50. Van Gogh energizes the night sky creating movement to enliven the painting.

51. The tail’s spiral follows the
curve of the Nautilus seashell.

52. Golden Rectangle
composition. The double doors
form a square. The main spiral
fits in the Golden Proportion left
door. The spiral follows the same
pattern of the Nautilus seashell.
The spiral is a wrought iron rod
raised ½” off the doors.

53. Bathroom wall tile Fibonacci Numbers Whirling Squares: 1, 2, 3, 5, 8, 13,
21.

54. The diagonal offset provides vitality and movement as it leads to the ceiling cut out
and hood. The knobs and handles emphasize the diagonal. If the arch continued as a
circle, it would touch at the corners of the cabinet near the middle knob and handle.

55. The design thrusts to the hood as the diagonal knobs and handles are

56. The dynamic quality of this building in Germany by Zaha Hadid has energy similar to
the previous kitchen. Where do you get your inspiration?

57. Mark Rosenhaus, CKD
568 Columbus Avenue
New York, NY 10024
Phone: 212-579-4598
Fax: 212-579-4599
Rosenhausdesign.com
Rosenhausdesign@gmail.com
ROSENHAUS DESIGN GROUP